Conventionally, the axial forces of threaded bolts have been controlled according to the fastening torques, and torque wrenches of various sorts have been widely used for this purpose. In this method, the axial force is simply estimated from the fastening torque. But according to this method, the estimated axial force may be a poor approximation of the actual value depending on the circumstances. Certain torque coefficients may be taken into account to compensate for various external factors. However, since the selection of appropriate torque coefficients is very critical for accurate estimation of the axial force and the torque coefficients are very much affected by various factors such as the dimensional precision of the threaded portion of the bolt and the condition of the seat surface of the bolt head, the general surface conditions of the members to be fastened, the lubrication conditions and so on, which could vary a great deal depending on the circumstances, it is difficult to achieve a high level of accuracy.
Japanese patent laid-open publication No. 50-140178 discloses a method of turning an already fastened threaded bolt or a nut over a certain angle and estimating the axial force in the bolt according to a calibration curve which gives the relationship between this angle and the axial force. According to this method, the measured values of the axial force are not affected by external factors so much as the method which depends on the torque coefficient, and an axial force measurement of a relatively high precision is possible. However, according to this method, the conditions preceding the turning of the bolt or the nut are required to be adjusted according to certain torque control criteria which are based on the concept of the so-called snug torque and controlling these conditions presents a major problem.
Japanese patent laid-open publication No. 61-19572 discloses a method of controlling the axial force based on the torque gradient method which basically involves the detection of the beginning of the plastic range of the deformation of the bolt. This method is based on the intrinsic characteristics of the material of the bolt itself but, at the same time, requires the recording of the change in the torque coefficient and the axial force must be estimated from this torque coefficient. Therefore, this method cannot necessarily assure a sufficiently high level of accuracy.
Japanese patent laid-open publication 51-43180 discloses a method of estimating the axial force of a bolt according to the change in the resonance frequency of the bolt which is known to change according to the state of stress in the bolt. This method is very powerful in theory but there are some problems with the detection accuracy of the sensor and the reproducibility of the conditions of radiation and reflection of ultrasonic sound tends to be poor. Therefore, achieving a high level of accuracy with this method is difficult. Also, this method requires expensive facilities and equipment for measurement.